Partial Differential Equations

ivan gabrovski

Iqukethe izikhangiso

Mayelana nalolu hlelo lokusebenza

Izilinganiso Zokuhlukaniswa Okungaphelele Kohlelo Lokusebenza
I-PDE iyi-equation ehilela ama-derivative angaphelele omsebenzi ongaziwa wezinto eziningana eziguquguqukayo (ngokuvamile isikhala kanye/noma isikhathi).
Ifomu Elijwayelekile: F(x,y,u,u_dx, u_dy, ...)=0
Komsebenzi u(x, y) noma u(x, t):
Ukuhlukaniswa Ngokwe-oda
I-oda lokuqala -” liqukethe ama-derivative angaphelele okuqala kuphela
I-oda lesibili - elivame kakhulu kwi-physics (ukushisa, amagagasi, amandla)
Izinhlobo Ezintathu Zakudala (eziqondile, ezilandelanayo, ezilandelanayo zesibili)
1. I-equation yokushisa/yokusabalalisa okufana noku ... I-equation yokuqhuba ukushisa (ebizwa nangokuthi i-diffusion equation) ichaza ukuthi izinga lokushisa lisakazeka kanjani ngokusebenzisa i-medium ngokuhamba kwesikhathi.
I-equation yamagagasi ichaza ukusabalala kokuphazamiseka (ukudlidliza, umsindo, ukukhanya, amagagasi amanzi) ngokusebenzisa i-medium ngesivinini esilinganiselwe.
I-equation ye-elliptic ichaza ukucushwa kokulingana kwe-steady-state (okungaxhomekeki ngesikhathi) — hhayi ukuvela ngokuhamba kwesikhathi. Isibonelo esivamile yi-equation kaLaplace/Poisson.
Izindlela Eziyinhloko Zesixazululo
Ukuhlukaniswa kweziguquguquki kuthatha u(x,t) = X(x)T(t)
Indlela yezimpawu noma i-first-order equation
I-Integral iguqula i-Fourier, i-Laplace
Imisebenzi kaGreen
Izindlela zezinombolo - umehluko olinganiselwe, izakhi ezilinganiselwe (ezimweni ezingenazo izixazululo zefomu elivaliwe)
Uhlelo lokusebenza lusebenzisa izindlela zezinombolo ze-heat, wave kanye ne-elliptic equations Futhi lushintsha amapharamitha kungxoxo. Imiphumela iboniswa ngemidwebo nangamapharamitha.